Radially-continuous operators on the Fock space

TL;DR

This paper characterizes a class of radially-continuous operators on the Fock space as band-dominated operators on ()), showing their relation to Toeplitz algebra and off-diagonal matrix properties.

Contribution

It establishes a correspondence between radially-continuous operators on the Fock space and band-dominated operators on ()), including their intersection with Toeplitz algebra.

Findings

Operators correspond to band-dominated matrices with square-root metric continuity.

Intersection with Toeplitz algebra characterized by off-diagonals with uniform square-root metric continuity.

Provides a new operator-theoretic framework linking Fock space operators to ()) matrices.

Abstract

We study operators on the Fock space on which by adjoining the rotation operators implements a continuous action of the circle group. We prove that this class of operators can be identified with the space of band-dominated operators on $\ell^2(\mathbb N_0)$ by mapping the operators to their matrix representations with respect to the standard orthonormal basis. Further, we prove that the intersection of this class with the Toeplitz algebra of the Fock space agrees, in the same manner, with the band-dominated operators on $\ell^2(\mathbb N_0)$ such that the off-diagonals of the matrix are sequences which are uniformly continuous with respect to the square-root metric.